Problem: Solve for $x$ and $y$ using elimination. ${5x+2y = 36}$ ${4x-2y = 18}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $9x = 54$ $\dfrac{9x}{{9}} = \dfrac{54}{{9}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {5x+2y = 36}\thinspace$ to find $y$ ${5}{(6)}{ + 2y = 36}$ $30+2y = 36$ $30{-30} + 2y = 36{-30}$ $2y = 6$ $\dfrac{2y}{{2}} = \dfrac{6}{{2}}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {4x-2y = 18}\thinspace$ and get the same answer for $y$ : ${4}{(6)}{ - 2y = 18}$ ${y = 3}$